%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN386^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:41:42 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN386^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:15:16 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.28 % (1863547)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1863555)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3276450544:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.28 % (1863555) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1863547-1863555"...
% 0.22/0.28 % (1863558)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (1863558)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (1863555)...printing done.
% 0.22/0.28 % (1863555)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, cD: ($i > $i > $i > $o)).
% 0.22/0.28 thf(func_def_1, type, cF: ($i > $i > $o)).
% 0.22/0.28 thf(func_def_2, type, cS: ($i > $i > $o)).
% 0.22/0.28 thf(func_def_7, type, sK1: ($i > $i)).
% 0.22/0.28 thf(func_def_8, type, sK2: ($i > $i)).
% 0.22/0.28 thf(func_def_9, type, sK3: ($i > $i)).
% 0.22/0.28 thf(func_def_10, type, sK4: ($i > $i)).
% 0.22/0.28 thf(func_def_11, type, sK5: ($i > $i > $i)).
% 0.22/0.28 thf(func_def_12, type, sK6: ($i > $i > $i)).
% 0.22/0.28 thf(f1,conjecture,(
% 0.22/0.28 (! [X0 : $i] : ? [X1 : $i] : (cF @ X0 @ X1) & ? [X0 : $i] : ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((cS @ X3 @ X4) => (cD @ X4 @ X0 @ X2)) & ! [X2 : $i] : ? [X5 : $i] : ! [X6 : $i,X7 : $i] : ((cD @ X6 @ X7 @ X5) => ! [X8 : $i,X1 : $i] : (((cF @ X6 @ X1) & (cF @ X7 @ X8)) => (cD @ X1 @ X8 @ X2)))) => ? [X1 : $i] : ! [X2 : $i] : ? [X9 : $i] : ! [X4 : $i] : ((cS @ X9 @ X4) => ! [X8 : $i] : ((cF @ X4 @ X8) => (cD @ X8 @ X1 @ X2)))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2138)).
% 0.22/0.28 thf(f2,negated_conjecture,(
% 0.22/0.28 ~((! [X0 : $i] : ? [X1 : $i] : (cF @ X0 @ X1) & ? [X0 : $i] : ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((cS @ X3 @ X4) => (cD @ X4 @ X0 @ X2)) & ! [X2 : $i] : ? [X5 : $i] : ! [X6 : $i,X7 : $i] : ((cD @ X6 @ X7 @ X5) => ! [X8 : $i,X1 : $i] : (((cF @ X6 @ X1) & (cF @ X7 @ X8)) => (cD @ X1 @ X8 @ X2)))) => ? [X1 : $i] : ! [X2 : $i] : ? [X9 : $i] : ! [X4 : $i] : ((cS @ X9 @ X4) => ! [X8 : $i] : ((cF @ X4 @ X8) => (cD @ X8 @ X1 @ X2))))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.28 thf(f3,plain,(
% 0.22/0.28 ~((! [X0 : $i] : ? [X1 : $i] : (cF @ X0 @ X1) & ? [X2 : $i] : ! [X3 : $i] : ? [X4 : $i] : ! [X5 : $i] : ((cS @ X4 @ X5) => (cD @ X5 @ X2 @ X3)) & ! [X6 : $i] : ? [X7 : $i] : ! [X8 : $i,X9 : $i] : ((cD @ X8 @ X9 @ X7) => ! [X10 : $i,X11 : $i] : (((cF @ X8 @ X11) & (cF @ X9 @ X10)) => (cD @ X11 @ X10 @ X6)))) => ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : ((cS @ X14 @ X15) => ! [X16 : $i] : ((cF @ X15 @ X16) => (cD @ X16 @ X12 @ X13))))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f4,plain,(
% 0.22/0.28 ~((! [X6 : $i] : ? [X7 : $i] : ! [X9 : $i,X8 : $i] : ((((cD @ X8 @ X9 @ X7)) = $true) => ! [X11 : $i,X10 : $i] : (((((cF @ X9 @ X10)) = $true) & ($true = ((cF @ X8 @ X11)))) => (((cD @ X11 @ X10 @ X6)) = $true))) & ? [X2 : $i] : ! [X3 : $i] : ? [X4 : $i] : ! [X5 : $i] : ((((cS @ X4 @ X5)) = $true) => (((cD @ X5 @ X2 @ X3)) = $true)) & ! [X0 : $i] : ? [X1 : $i] : (((cF @ X0 @ X1)) = $true)) => ? [X12 : $i] : ! [X13 : $i] : ? [X14 : $i] : ! [X15 : $i] : (($true = ((cS @ X14 @ X15))) => ! [X16 : $i] : ((((cF @ X15 @ X16)) = $true) => ($true = ((cD @ X16 @ X12 @ X13))))))),
% 0.22/0.28 inference(fool_elimination,[],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 ! [X12 : $i] : ? [X13 : $i] : ! [X14 : $i] : ? [X15 : $i] : (($true = ((cS @ X14 @ X15))) & ? [X16 : $i] : (($true != ((cD @ X16 @ X12 @ X13))) & (((cF @ X15 @ X16)) = $true))) & (! [X6 : $i] : ? [X7 : $i] : ! [X9 : $i,X8 : $i] : (! [X11 : $i,X10 : $i] : ((((cD @ X11 @ X10 @ X6)) = $true) | ((((cF @ X9 @ X10)) != $true) | ($true != ((cF @ X8 @ X11))))) | (((cD @ X8 @ X9 @ X7)) != $true)) & ? [X2 : $i] : ! [X3 : $i] : ? [X4 : $i] : ! [X5 : $i] : ((((cD @ X5 @ X2 @ X3)) = $true) | (((cS @ X4 @ X5)) != $true)) & ! [X0 : $i] : ? [X1 : $i] : (((cF @ X0 @ X1)) = $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f4])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 ? [X2 : $i] : ! [X3 : $i] : ? [X4 : $i] : ! [X5 : $i] : ((((cD @ X5 @ X2 @ X3)) = $true) | (((cS @ X4 @ X5)) != $true)) & ! [X0 : $i] : ? [X1 : $i] : (((cF @ X0 @ X1)) = $true) & ! [X6 : $i] : ? [X7 : $i] : ! [X8 : $i,X9 : $i] : ((((cD @ X8 @ X9 @ X7)) != $true) | ! [X11 : $i,X10 : $i] : (($true != ((cF @ X8 @ X11))) | (((cF @ X9 @ X10)) != $true) | (((cD @ X11 @ X10 @ X6)) = $true))) & ! [X12 : $i] : ? [X13 : $i] : ! [X14 : $i] : ? [X15 : $i] : (($true = ((cS @ X14 @ X15))) & ? [X16 : $i] : (($true != ((cD @ X16 @ X12 @ X13))) & (((cF @ X15 @ X16)) = $true)))),
% 0.22/0.28 inference(flattening,[],[f5])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : ! [X3 : $i] : ((((cD @ X3 @ X0 @ X1)) = $true) | (((cS @ X2 @ X3)) != $true)) & ! [X4 : $i] : ? [X5 : $i] : (((cF @ X4 @ X5)) = $true) & ! [X6 : $i] : ? [X7 : $i] : ! [X8 : $i,X9 : $i] : ((((cD @ X8 @ X9 @ X7)) != $true) | ! [X10 : $i,X11 : $i] : ((((cF @ X8 @ X10)) != $true) | (((cF @ X9 @ X11)) != $true) | (((cD @ X10 @ X11 @ X6)) = $true))) & ! [X12 : $i] : ? [X13 : $i] : ! [X14 : $i] : ? [X15 : $i] : (($true = ((cS @ X14 @ X15))) & ? [X16 : $i] : (($true != ((cD @ X16 @ X12 @ X13))) & (((cF @ X15 @ X16)) = $true)))),
% 0.22/0.28 inference(rectify,[],[f6])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ! [X1 : $i] : ! [X3 : $i] : ((((cD @ X3 @ sK0 @ X1)) = $true) | (((cS @ (sK1 @ X1) @ X3)) != $true)) & ! [X4 : $i] : ($true = ((cF @ X4 @ (sK2 @ X4)))) & ! [X6 : $i] : ! [X8 : $i,X9 : $i] : (($true != ((cD @ X8 @ X9 @ (sK3 @ X6)))) | ! [X10 : $i,X11 : $i] : ((((cF @ X8 @ X10)) != $true) | (((cF @ X9 @ X11)) != $true) | (((cD @ X10 @ X11 @ X6)) = $true))) & ! [X12 : $i] : ! [X14 : $i] : (($true = ((cS @ X14 @ (sK5 @ X14 @ X12)))) & ((((cD @ (sK6 @ X14 @ X12) @ X12 @ (sK4 @ X12))) != $true) & (((cF @ (sK5 @ X14 @ X12) @ (sK6 @ X14 @ X12))) = $true)))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X16,sK6 @ X14 @ X12),skolemize(X16,sK6 @ X14 @ X12),skolemize(X16,sK6 @ X14 @ X12),skolemize(X16,sK6 @ X14 @ X12),skolemize(X16,sK6 @ X14 @ X12),skolemize(X16,sK6 @ X14 @ X12)],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ( ! [X14 : $i,X12 : $i] : ((((cF @ (sK5 @ X14 @ X12) @ (sK6 @ X14 @ X12))) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ( ! [X14 : $i,X12 : $i] : ((((cD @ (sK6 @ X14 @ X12) @ X12 @ (sK4 @ X12))) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ( ! [X14 : $i,X12 : $i] : (($true = ((cS @ X14 @ (sK5 @ X14 @ X12))))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ( ! [X10 : $i,X11 : $i,X8 : $i,X6 : $i,X9 : $i] : (($true != ((cD @ X8 @ X9 @ (sK3 @ X6)))) | (((cF @ X8 @ X10)) != $true) | (((cF @ X9 @ X11)) != $true) | (((cD @ X10 @ X11 @ X6)) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 ( ! [X4 : $i] : (($true = ((cF @ X4 @ (sK2 @ X4))))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 ( ! [X3 : $i,X1 : $i] : ((((cD @ X3 @ sK0 @ X1)) = $true) | (((cS @ (sK1 @ X1) @ X3)) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f18,plain,(
% 0.22/0.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((cF @ sK0 @ X3))) | ($true != ((cF @ X0 @ X2))) | (((cD @ X2 @ X3 @ X1)) = $true) | ($true != $true) | ($true != ((cS @ (sK1 @ (sK3 @ X1)) @ X0)))) )),
% 0.22/0.28 inference(superposition,[],[f12,f14])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((cD @ X2 @ X3 @ X1)) = $true) | ($true != ((cF @ X0 @ X2))) | ($true != ((cF @ sK0 @ X3))) | ($true != ((cS @ (sK1 @ (sK3 @ X1)) @ X0)))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f18])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((cS @ (sK1 @ (sK3 @ (sK4 @ X1))) @ X2)) != $true) | (((cF @ sK0 @ X1)) != $true) | (((cF @ X2 @ (sK6 @ X0 @ X1))) != $true)) )),
% 0.22/0.28 inference(superposition,[],[f10,f19])).
% 0.22/0.28 thf(f22,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cS @ (sK1 @ (sK3 @ (sK4 @ X1))) @ X2)) != $true) | (((cF @ X2 @ (sK6 @ X0 @ X1))) != $true) | (((cF @ sK0 @ X1)) != $true)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f21])).
% 0.22/0.28 thf(f30,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((cF @ (sK5 @ (sK1 @ (sK3 @ (sK4 @ X0))) @ X1) @ (sK6 @ X2 @ X0))) != $true) | (((cF @ sK0 @ X0)) != $true)) )),
% 0.22/0.28 inference(superposition,[],[f22,f11])).
% 0.22/0.28 thf(f31,plain,(
% 0.22/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cF @ (sK5 @ (sK1 @ (sK3 @ (sK4 @ X0))) @ X1) @ (sK6 @ X2 @ X0))) != $true) | (((cF @ sK0 @ X0)) != $true)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f30])).
% 0.22/0.28 thf(f36,plain,(
% 0.22/0.28 ( ! [X0 : $i] : ((((cF @ sK0 @ X0)) != $true) | ($true != $true)) )),
% 0.22/0.28 inference(superposition,[],[f31,f9])).
% 0.22/0.28 thf(f37,plain,(
% 0.22/0.28 ( ! [X0 : $i] : ((((cF @ sK0 @ X0)) != $true)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f36])).
% 0.22/0.28 thf(f38,plain,(
% 0.22/0.28 ($true != $true)),
% 0.22/0.28 inference(superposition,[],[f37,f13])).
% 0.22/0.28 thf(f39,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f38])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (1863555)------------------------------
% 0.22/0.28 % (1863555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1863555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1863555)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1863555)Termination reason: Refutation
% 0.22/0.28 % (1863555)Time elapsed: 0.004 s
% 0.22/0.28 % (1863555)Peak memory usage: 12 MB
% 0.22/0.28 % (1863555)Instructions burned: 9 (million)
% 0.22/0.28 % (1863547)Success in time 0.03 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------